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Elin
Registered User regular

I have no clue how to graph for i. Really, I searched my book, my lecture notes, the internet. I'm turning to you, please tell me how to graph for imaginary numbers.

The problem I'm presenting is not the actual problem I'm doing, but it's similar.

f(x)=(x+2)^2(x-3)(x-(2+i))(x-(2-i))

I can graph fine until I get the the imaginary set. I don't even know how to punch it into a graphing calculator to try and figure it out that way. In fact, I don't own a graphing calculator. My college doesn't allow their use on tests so I always figured it was a waste of cash to buy one.

The problem I'm presenting is not the actual problem I'm doing, but it's similar.

f(x)=(x+2)^2(x-3)(x-(2+i))(x-(2-i))

I can graph fine until I get the the imaginary set. I don't even know how to punch it into a graphing calculator to try and figure it out that way. In fact, I don't own a graphing calculator. My college doesn't allow their use on tests so I always figured it was a waste of cash to buy one.

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## Posts

Since they are complex conjugates we can obtain the form (x-2)^2 + 1. This is completely real. Is the problem to graph the whole expression by hand?

MerouanonElinonSwitch SW-5832-5050-0149PSN Hypacia

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The thing is, although this function looks like it'll spit out complex numbers, it wont, because the two complex roots are complex conjugates of each other (meaning they are related to each other by multiplying the imaginary part of one root by -1. this gives you the other root). Explicitly, you get

f(x) = (x-2)^2 (x-3) (x^2 -4x +5).

How do you usually graph functions? I'm not sure how you are expected to graph polynomial functions with purely real roots even... if what I gave you before isn't enough to help you, can you tell us how you usually graph them? Do you look for the roots and plug in numbers around it to find the behavior, or do you know calculus?

Merouanon